Ladder operators and coherent states for continuous spectra

TL;DR

This paper introduces ladder operators for systems with continuous spectra and defines coherent states as modified eigenvectors, maintaining Gazeau-Klauder axioms, expanding the theoretical framework of quantum states.

Contribution

It develops a new approach to defining ladder operators and coherent states for continuous spectrum systems, preserving established axioms.

Findings

Defined two types of annihilation operators for continuous spectra

Constructed coherent states as modified eigenvectors of these operators

Maintained Gazeau-Klauder axioms in the new framework

Abstract

The notion of ladder operators is introduced for systems with continuous spectra. We identify two different kinds of annihilation operators allowing the definition of coherent states as modified "eigenvectors" of these operators. Axioms of Gazeau-Klauder are maintained throughout the construction.